A Family of Derivative Free Algorithms for Multiple-Roots of Van Der Waals Problem

Abstract

There are a good number of higher-order iterative methods for computing multiple zeros of nonlinear equations in the available literature. Most of them required first or higher-order derivatives of the involved function. No doubt, high-order derivative-free methods for multiple zeros are more difficult to obtain in comparison with simple zeros and with first order derivatives. This study presents an optimal family of fourth order derivative-free techniques for multiple zeros that requires just three evaluations of function ϕ, per iteration. The approximations of the derivative/s are based on symmetric divided differences. We also demonstrate the application of new algorithms on Van der Waals, Planck law radiation, Manning for isentropic supersonic flow and complex root problems. Numerical results reveal that the proposed derivative-free techniques are more efficient in comparison terms of CPU, residual error, computational order of convergence, number of iterations and the difference between two consecutive iterations with other existing methods.